| A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY |
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| 作者姓名： | Zhang Zhennan Ge Xiurun Li Yonghe |
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| 作者单位： | Zhang Zhennan Ge Xiurun Li Yonghe (Department of Civil Engineering，Shanghai University，Shanghai 200072，China) (Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，China) (Institute of Geotechnical Engineering，Shanghai Jiaotong University，Shanghai 200030，China) (Institute of Rock and Soil Mechanics，the Chinese Academy of Sciences，Wuhan 430071，China) |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson's ratio and Young's modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds (VMIB) model, is proposed by incorporating a shear bond into the virtual internal bond (VIB) model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. Prom the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.
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| 关 键 词： | 虚拟多空间内结合 材料维度 多刻度模型 分子动力学 虚拟内结合 |
| 收稿时间： | 2005-12-29 |
| 修稿时间： | 2006-05-25 |
A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY |
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| Zhang Zhennan Ge Xiurun Li Yonghe.A MULTISCALE MECHANICAL MODEL FOR MATERIALS BASED ON VIRTUAL INTERNAL BOND THEORY[J].Acta Mechanica Solida Sinica,2006,19(3):196-202. |
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| Authors: | Zhang Zhennan Ge Xiurun Li Yonghe |
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| Institution: | 1. School of Mechanical Engineering, The University of Adelaide, South Australia SA 5005, Australia;2. Department of Management and Engineering, University of Padova, Stradella S. Nicola 3, 36100 Vicenza, Italy;3. School of Civil Engineering and Mining, The University of Adelaide, South Australia SA 5005, Australia;1. Department of Aeronautics, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, United Kingdom;2. Department of Mechanical Engineering, The University of Sheffield, Sir Frederick Mappin Building, Mappin Street, Sheffield S1 3JD, United Kingdom;3. Computer-Aided Aerospace & Mechanical Engineering (CA2M) Research Group, Sir Frederick Mappin Building, Mappin Street, Sheffield S1 3JD, United Kingdom;4. Industrial Doctorate Centre in Machining Science, The University of Sheffield, Sir Frederick Mappin Building, Mappin Street, Sheffield S1 3JD, United Kingdom |
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| Abstract: | Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson's ratio and Young's modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds (VMIB) model, is proposed by incorporating a shear bond into the virtual internal bond (VIB) model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. Prom the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found. |
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| Keywords: | virtual multi-dimensional internal bond material property dimensionality multiscale modeling molecular dynamics virtual internal bond |
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